A smooth introduction to some Algebraic Topology topics

Since the previous post on Grids touched some topics on algebraic topology, I  selected a few sites where I found some interesting information from our point of view that can help the reading of the previous slides and, in general, of the references already presented.

• This science4all site is a very visual and simple introduction to most of the concepts formalized in slides.
• Isabel Darcy's video lectures  on Applied Algebraic Topology are also enjoyable (You can stop anywhere but I put them all)
• On Euler's characteristics (We did not mention it in slides, but is worth to know)
• Simplicial, Addition, Orientation
• Modular Mathematics
• Addition and free vector spaces
• Triangulation and simplicial complexes
• Creating a simplicial complex from data 
• Persistent Homology  - I
• Persistent Homology - II
• Persistent Homology - III 
• A quick example calculating the column space and the nullspace of a matrix
•  Clustering via persistent Homology

 

• Enzo Tonti's lectures about his book

• The reasons of analogies in Physics - Part I - Part II - Part III - Part IV - Part V - Part VI

I do not share many of Tonti's opinions, but some of his talks and books are, indeed, enlightening.